We denote with \( \Sigma ^\phi (K) \)  the set of points in \( \mathbf {R}^{n} \operatorname{\sim }K \)  where \(\delta _{K}^{\phi } \)  is not differentiable. If \( K \)  is at least a \( \mathcal {C}^2\) -submanifold, then \( \delta _{K}^{\phi } \)  is at least of class \( \mathcal {C}^2 \)  on
the open subset \( \mathbf {R}^{n} \operatorname{\sim }\big (K \cup \mathop {\mathrm {Clos}}\Sigma ^\phi (K)) \)  and \(\mathop {\mathrm {Clos}}\Sigma ^\phi (K)\)  is a set of \(  {L}^{n} \) -measure zero; indeed if \( K \)  is \(\mathcal {C}^{2,1} \) -submanifold, then \(\mathop {\mathrm {Clos}}\Sigma ^\phi (K)\)  is a set of locally
finite \(  {H}^{n-1}  \) -measure. See [1]}, [2]},
[3]}, [4]} and [5]}. A sufficient condition
that guarantees \(  {L}^{n}(\mathop {\mathrm {Clos}}\Sigma (K)) =0 \)  for closed \(\mathcal {C}^{1,1} \) -hypersurfaces is contained in [6]}.
